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Biophys J, September 2002, p. 1380-1394, Vol. 83, No. 3

Calculation of Forces at Focal Adhesions from Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization

U. S. Schwarz,*dagger N. Q. Balaban,Dagger § D. Riveline,§ A. Bershadsky,§ B. Geiger,§ and S. A. Safrandagger

 *Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany;  dagger Department of Materials and Interfaces, The Weizmann Institute of Science, Rehovot 76100, Israel;  Dagger Laboratory of Living Matter, Rockefeller University, New York, New York 10021 USA;  §Department of Molecular Cell Biology, The Weizmann Institute of Science, Rehovot 76100, Israel; and  Laboratoire de Spectrométrie Physique, UMR 5588, Université Joseph Fourier-CNRS, BP 87, 38402 Saint Martin d'Hères Cedex, France

Forces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time.

Biophys J, September 2002, p. 1380-1394, Vol. 83, No. 3
© 2002 by the Biophysical Society   0006-3495/02/09/1380/15  $2.00


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